Abbott - Flatland a Romance of Many Dimensions

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Flatland: A Romance of Many DimensionsAbbott, Edwin Abbott

Published: 1884Categorie(s): Fiction, Humorous, Non-Fiction, Philosophy, ScienceSource: http://gutenberg.org

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About Abbott:Edwin Abbott Abbott (December 20, 1838 October 12, 1926), English

schoolmaster and theologian, is best known as the author of the mathem-atical satire and religious allegory Flatland (1884). Abbott was the eldest

son of Edwin Abbott (18081882), headmaster of the Philological School,Marylebone, and his wife, Jane Abbott (18061882). His parents werefirst cousins. He was educated at the City of London School and at St

John's College, Cambridge, where he took the highest honours in clas-sics, mathematics and theology, and became fellow of his college. In 1862he took orders. After holding masterships at King Edward's School,Birmingham, and at Clifton College, he succeeded G. F. Mortimer asheadmaster of the City of London School in 1865 at the early age oftwenty-six. He was Hulsean lecturer in 1876. He retired in 1889, and de-

voted himself to literary and theological pursuits. Dr. Abbott's liberal in-clinations in theology were prominent both in his educational views andin his books. His Shakespearian Grammar (1870) is a permanent contri-

bution to English philology. In 1885 he published a life of Francis Bacon.His theological writings include three anonymously published religiousromances - Philochristus (1878), Onesimus (1882), and Sitanus (1906).More weighty contributions are the anonymous theological discussionThe Kernel and the Husk (1886), Philomythus (1891), his book TheAnglican Career of Cardinal Newman (1892), and his article "The

Gospels" in the ninth edition of the Encyclopdia Britannica, embodyinga critical view which caused considerable stir in the English theologicalworld. He also wrote St Thomas of Canterbury, his Death and Miracles(1898), Johannine Vocabulary (1905), Johannine Grammar (1906). Flat-land was published in 1884. Source: Wikipedia

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Part 1This World

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Chapter 1Of the Nature of Flatland

I call our world Flatland, not because we call it so, but to make its natureclearer to you, my happy readers, who are privileged to live in Space.

Imagine a vast sheet of paper on which straight Lines, Triangles,

Squares, Pentagons, Hexagons, and other figures, instead of remainingfixed in their places, move freely about, on or in the surface, but withoutthe power of rising above or sinking below it, very much like shad-owsonly hard with luminous edgesand you will then have a prettycorrect notion of my country and countrymen. Alas, a few years ago, Ishould have said "my universe:" but now my mind has been opened tohigher views of things. In such a country, you will perceive at once thatit is impossible that there should be anything of what you call a "solid"kind; but I dare say you will suppose that we could at least distinguish

by sight the Triangles, Squares, and other figures, moving about as Ihave described them. On the contrary, we could see nothing of the kind,not at least so as to distinguish one figure from another. Nothing wasvisible, nor could be visible, to us, except Straight Lines; and the neces-sity of this I will speedily demonstrate.

Place a penny on the middle of one of your tables in Space; and lean-ing over it, look down upon it. It will appear a circle.

But now, drawing back to the edge of the table, gradually lower youreye (thus bringing yourself more and more into the condition of the in-

habitants of Flatland), and you will find the penny becoming more andmore oval to your view, and at last when you have placed your eye ex-actly on the edge of the table (so that you are, as it were, actually a Flat-lander) the penny will then have ceased to appear oval at all, and willhave become, so far as you can see, a straight line.

The same thing would happen if you were to treat in the same way aTriangle, or a Square, or any other figure cut out from pasteboard. Assoon as you look at it with your eye on the edge of the table, you willfind that it ceases to appear to you as a figure, and that it becomes in

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appearance a straight line. Take for example an equilateral Tri-anglewho represents with us a Tradesman of the respectable class. Fig-ure 1 represents the Tradesman as you would see him while you were

bending over him from above; figures 2 and 3 represent the Tradesman,

as you would see him if your eye were close to the level, or all but on thelevel of the table; and if your eye were quite on the level of the table (andthat is how we see him in Flatland) you would see nothing but a straightline.

When I was in Spaceland I heard that your sailors have very similarexperiences while they traverse your seas and discern some distant is-land or coast lying on the horizon. The far-off land may have bays, fore-lands, angles in and out to any number and extent; yet at a distance yousee none of these (unless indeed your sun shines bright upon them re-

vealing the projections and retirements by means of light and shade),nothing but a grey unbroken line upon the water.

Well, that is just what we see when one of our triangular or other ac-quaintances comes towards us in Flatland. As there is neither sun withus, nor any light of such a kind as to make shadows, we have none of thehelps to the sight that you have in Spaceland. If our friend comes closerto us we see his line becomes larger; if he leaves us it becomes smaller;

but still he looks like a straight line; be he a Triangle, Square, Pentagon,Hexagon, Circle, what you will a straight Line he looks and nothing

else.You may perhaps ask how under these disadvantagous circumstances

we are able to distinguish our friends from one another: but the answerto this very natural question will be more fitly and easily given when Icome to describe the inhabitants of Flatland. For the present let me deferthis subject, and say a word or two about the climate and houses in ourcountry.

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Chapter 2Of the Climate and Houses in Flatland

As with you, so also with us, there are four points of the compass North,South, East, and West.

There being no sun nor other heavenly bodies, it is impossible for us to

determine the North in the usual way; but we have a method of our own.By a Law of Nature with us, there is a constant attraction to the South;and, although in temperate climates this is very slight so that even aWoman in reasonable health can journey several furlongs northwardwithout much difficulty yet the hampering effort of the southward at-traction is quite sufficient to serve as a compass in most parts of ourearth. Moreover, the rain (which falls at stated intervals) coming alwaysfrom the North, is an additional assistance; and in the towns we have theguidance of the houses, which of course have their side-walls running

for the most part North and South, so that the roofs may keep off the rainfrom the North. In the country, where there are no houses, the trunks ofthe trees serve as some sort of guide. Altogether, we have not so muchdifficulty as might be expected in determining our bearings.

Yet in our more temperate regions, in which the southward attractionis hardly felt, walking sometimes in a perfectly desolate plain wherethere have been no houses nor trees to guide me, I have been occasion-ally compelled to remain stationary for hours together, waiting till therain came before continuing my journey. On the weak and aged, and es-

pecially on delicate Females, the force of attraction tells much moreheavily than on the robust of the Male Sex, so that it is a point of breed-ing, if you meet a Lady on the street, always to give her the North side ofthe wayby no means an easy thing to do always at short notice whenyou are in rude health and in a climate where it is difficult to tell yourNorth from your South.

Windows there are none in our houses: for the light comes to us alikein our homes and out of them, by day and by night, equally at all timesand in all places, whence we know not. It was in old days, with our

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learned men, an interesting and oft-investigate question, "What is theorigin of light?" and the solution of it has been repeatedly attempted,with no other result than to crowd our lunatic asylums with the would-

be solvers. Hence, after fruitless attempts to suppress such investigations

indirectly by making them liable to a heavy tax, the Legislature, in com-paratively recent times, absolutely prohibited them. Ialas, I alone inFlatlandknow now only too well the true solution of this mysteriousproblem; but my knowledge cannot be made intelligible to a single oneof my countrymen; and I am mocked at I, the sole possessor of thetruths of Space and of the theory of the introduction of Light from theworld of three Dimensionsas if I were the maddest of the mad! But atruce to these painful digressions: let me return to our homes.

The most common form for the construction of a house is five-sided or

pentagonal, as in the annexed figure. The two Northern sides RO, OF,constitute the roof, and for the most part have no doors; on the East is asmall door for the Women; on the West a much larger one for the Men;the South side or floor is usually doorless.

Square and triangular houses are not allowed, and for this reason. Theangles of a Square (and still more those of an equilateral Triangle,) beingmuch more pointed than those of a Pentagon, and the lines of inanimateobjects (such as houses) being dimmer than the lines of Men and Wo-men, it follows that there is no little danger lest the points of a square of

triangular house residence might do serious injury to an inconsiderate orperhaps absentminded traveller suddenly running against them: andtherefore, as early as the eleventh century of our era, triangular houseswere universally forbidden by Law, the only exceptions beingfortifications, powder-magazines, barracks, and other state buildings,which is not desirable that the general public should approach withoutcircumspection.

At this period, square houses were still everywhere permitted, thoughdiscouraged by a special tax. But, about three centuries afterwards, theLaw decided that in all towns containing a population above ten thou-sand, the angle of a Pentagon was the smallest house-angle that could beallowed consistently with the public safety. The good sense of the com-munity has seconded the efforts of the Legislature; and now, even in thecountry, the pentagonal construction has superseded every other. It isonly now and then in some very remote and backward agricultural dis-trict that an antiquarian may still discover a square house.

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Chapter 3Concerning the Inhabitants of Flatland

The greatest length or breadth of a full grown inhabitant of Flatland maybe estimated at about eleven of your inches. Twelve inches may be re-garded as a maximum.

Our Women are Straight Lines.Our Soldiers and Lowest Class of Workmen are Triangles with two

equal sides, each about eleven inches long, and a base or third side soshort (often not exceeding half an inch) that they form at their vertices avery sharp and formidable angle. Indeed when their bases are of themost degraded type (not more than the eighth part of an inch in size),they can hardly be distinguished from Straight lines or Women; so ex-tremely pointed are their vertices. With us, as with you, these Trianglesare distinguished from others by being called Isosceles; and by this name

I shall refer to them in the following pages.Our Middle Class consists of Equilateral or Equal-Sided Triangles.Our Professional Men and Gentlemen are Squares (to which class I

myself belong) and Five-Sided Figures or Pentagons.Next above these come the Nobility, of whom there are several de-

grees, beginning at Six-Sided Figures, or Hexagons, and from thencerising in the number of their sides till they receive the honourable title ofPolygonal, or many-Sided. Finally when the number of the sides be-comes so numerous, and the sides themselves so small, that the figure

cannot be distinguished from a circle, he is included in the Circular orPriestly order; and this is the highest class of all.

It is a Law of Nature with us that a male child shall have one moreside than his father, so that each generation shall rise (as a rule) one stepin the scale of development and nobility. Thus the son of a Square is aPentagon; the son of a Pentagon, a Hexagon; and so on.

But this rule applies not always to the Tradesman, and still less oftento the Soldiers, and to the Workmen; who indeed can hardly be said todeserve the name of human Figures, since they have not all their sides

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equal. With them therefore the Law of Nature does not hold; and the sonof an Isosceles (i.e. a Triangle with two sides equal) remains Isoscelesstill. Nevertheless, all hope is not such out, even from the Isosceles, thathis posterity may ultimately rise above his degraded condition. For, after

a long series of military successes, or diligent and skillful labours, it isgenerally found that the more intelligent among the Artisan and Soldierclasses manifest a slight increase of their third side or base, and a shrink-age of the two other sides. Intermarriages (arranged by the Priests)

between the sons and daughters of these more intellectual members ofthe lower classes generally result in an offspring approximating stillmore to the type of the Equal-Sided Triangle.

Rarelyin proportion to the vast numbers of Isosceles births is agenuine and certifiable Equal-Sided Triangle produced from Isosceles

parents1. Such a birth requires, as its antecedents, not only a series of carefully

arranged intermarriages, but also a long-continued exercise of frugalityand self-control on the part of the would-be ancestors of the comingEquilateral, and a patient, systematic, and continuous development ofthe Isosceles intellect through many generations.

The birth of a True Equilateral Triangle from Isosceles parents is thesubject of rejoicing in our country for many furlongs round. After a strictexamination conducted by the Sanitary and Social Board, the infant, if

certified as Regular, is with solemn ceremonial admitted into the class ofEquilaterals. He is then immediately taken from his proud yet sorrowingparents and adopted by some childless Equilateral, who is bound byoath never to permit the child henceforth to enter his former home or somuch as to look upon his relations again, for fear lest the freshly de-veloped organism may, by force of unconscious imitation, fall back againinto his hereditary level.

The occasional emergence of an Equilateral from the ranks of his serf-born ancestors is welcomed, not only by the poor serfs themselves, as agleam of light and hope shed upon the monotonous squalor of their ex-istence, but also by the Aristocracy at large; for all the higher classes arewell aware that these rare phenomena, while they do little or nothing to

1."What need of a certificate?" a Spaceland critic may ask: "Is not the procreation of aSquare Son a certificate from Nature herself, proving the Equal-sidedness of the Fath-er?" I reply that no Lady of any position will mary an uncertified Triangle. Squareoffspring has sometimes resulted from a slightly Irregular Triangle; but in almostevery such case the Irregularity of the first generation is visited on the third; which

either fails to attain the Pentagonal rank, or relapses to the Triangular.

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vulgarize their own privileges, serve as almost useful barrier against re-volution from below.

Had the acute-angled rabble been all, without exception, absolutelydestitute of hope and of ambition, they might have found leaders in

some of their many seditious outbreaks, so able as to render their superi-or numbers and strength too much even for the wisdom of the Circles.But a wise ordinance of Nature has decreed that in proportion as theworking-classes increase in intelligence, knowledge, and all virtue, inthat same proportion their acute angle (which makes them physicallyterrible) shall increase also and approximate to their comparativelyharmless angle of the Equilateral Triangle. Thus, in the most brutal andformidable off the soldier class creatures almost on a level with wo-men in their lack of intelligence it is found that, as they wax in the

mental ability necessary to employ their tremendous penetrating powerto advantage, so do they wane in the power of penetration itself.

How admirable is the Law of Compensation! And how perfect a proofof the natural fitness and, I may almost say, the divine origin of the aris-tocratic constitution of the States of Flatland! By a judicious use of thisLaw of Nature, the Polygons and Circles are almost always able to stiflesedition in its very cradle, taking advantage of the irrepressible and

boundless hopefulness of the human mind. Art also comes to the aid ofLaw and Order. It is generally found possibleby a little artificial com-

pression or expansion on the part of the State physiciansto make someof the more intelligent leaders of a rebellion perfectly Regular, and to ad-mit them at once into the privileged classes; a much larger number, whoare still below the standard, allured by the prospect of being ultimatelyennobled, are induced to enter the State Hospitals, where they are keptin honourable confinement for life; one or two alone of the most obstin-ate, foolish, and hopelessly irregular are led to execution.

Then the wretched rabble of the Isosceles, planless and leaderless, areether transfixed without resistance by the small body of their brethrenwhom the Chief Circle keeps in pay for emergencies of this kind; or elsemore often, by means of jealousies and suspicious skillfully fomentedamong them by the Circular party, they are stirred to mutual warfare,and perish by one another's angles. No less than one hundred andtwenty rebellions are recorded in our annals, besides minor outbreaksnumbered at two hundred and thirty-five; and they have all ended thus.

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Chapter 4Concerning the Women

If our highly pointed Triangles of the Soldier class are formidable, it maybe readily inferred that far more formidable are our Women. For, if a Sol-dier is a wedge, a Woman is a needle; being, so to speak, ALL point, at

least at the two extremities. Add to this the power of making herselfpractically invisible at will, and you will perceive that a Female, in Flat-land, is a creature by no means to be trifled with.

But here, perhaps, some of my younger Readers may ask HOW a wo-man in Flatland can make herself invisible. This ought, I think, to be ap-parent without any explanation. However, a few words will make itclear to the most unreflecting.

Place a needle on the table. Then, with your eye on the level of thetable, look at it side-ways, and you see the whole length of it; but look at

it end-ways, and you see nothing but a point, it has become practicallyinvisible. Just so is it with one of our Women. When her side is turned to-wards us, we see her as a straight line; when the end containing her eyeor mouthfor with us these two organs are identicalis the part thatmeets our eye, then we see nothing but a highly lustrous point; but whenthe back is presented to our view, thenbeing only sub-lustrous, and,indeed, almost as dim as an inanimate objecther hinder extremityserves her as a kind of Invisible Cap.

The dangers to which we are exposed from our Women must now be

manifest to the meanest capacity of Spaceland. If even the angle of a re-spectable Triangle in the middle class is not without its dangers; if to runagainst a Working Man involves a gash; if collision with an Officer of themilitary class necessitates a serious wound; if a mere touch from the ver-tex of a Private Soldier brings with it danger of death; what can it be torun against a woman, except absolute and immediate destruction? Andwhen a Woman is invisible, or visible only as a dim sub-lustrous point,how difficult must it be, even for the most cautious, always to avoidcollision!

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Many are the enactments made at different times in the different Statesof Flatland, in order to minimize this peril; and in the Southern and lesstemperate climates, where the force of gravitation is greater, and human

beings more liable to casual and involuntary motions, the Laws concern-

ing Women are naturally much more stringent. But a general view of theCode may be obtained from the following summary:

1. Every house shall have one entrance on the Eastern side, for the useof Females only; by which all females shall enter "in a becoming and re-spectful manner" and not by the Men's or Western door.

2. No Female shall walk in any public place without continually keep-ing up her Peace-cry, under penalty of death.

3. Any Female, duly certified to be suffering from St. Vitus's Dance,fits, chronic cold accompanied by violent sneezing, or any disease neces-

sitating involuntary motions, shall be instantly destroyed.In some of the States there is an additional Law forbidding Females,

under penalty of death, from walking or standing in any public placewithout moving their backs constantly from right to left so as to indicatetheir presence to those behind them; other oblige a Woman, when travel-ling, to be followed by one of her sons, or servants, or by her husband;others confine Women altogether in their houses except during the reli-gious festivals. But it has been found by the wisest of our Circles orStatesmen that the multiplication of restrictions on Females tends not

only to the debilitation and diminution of the race, but also to the in-crease of domestic murders to such an extent that a State loses more thanit gains by a too prohibitive Code.

For whenever the temper of the Women is thus exasperated by con-finement at home or hampering regulations abroad, they are apt to venttheir spleen upon their husbands and children; and in the less temperateclimates the whole male population of a village has been sometimes des-troyed in one or two hours of a simultaneous female outbreak. Hence theThree Laws, mentioned above, suffice for the better regulated States, andmay be accepted as a rough exemplification of our Female Code.

After all, our principal safeguard is found, not in Legislature, but inthe interests of the Women themselves. For, although they can inflict in-stantaneous death by a retrograde movement, yet unless they can at oncedisengage their stinging extremity from the struggling body of their vic-tim, their own frail bodies are liable to be shattered.

The power of Fashion is also on our side. I pointed out that in someless civilized States no female is suffered to stand in any public placewithout swaying her back from right to left. This practice has been

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universal among ladies of any pretensions to breeding in all well-gov-erned States, as far back as the memory of Figures can reach. It is con-sidered a disgrace to any state that legislation should have to enforcewhat ought to be, and is in every respectable female, a natural instinct.

The rhythmical and, if I may so say, well-modulated undulation of theback in our ladies of Circular rank is envied and imitated by the wife of acommon Equilateral, who can achieve nothing beyond a mere monoton-ous swing, like the ticking of a pendulum; and the regular tick of theEquilateral is no less admired and copied by the wife of the progressiveand aspiring Isosceles, in the females of whose family no "back-motion"of any kind has become as yet a necessity of life. Hence, in every familyof position and consideration, "back motion" is as prevalent as time itself;and the husbands and sons in these households enjoy immunity at least

from invisible attacks.Not that it must be for a moment supposed that our Women are desti-

tute of affection. But unfortunately the passion of the moment predomin-ates, in the Frail Sex, over every other consideration. This is, of course, anecessity arising from their unfortunate conformation. For as they haveno pretensions to an angle, being inferior in this respect to the very low-est of the Isosceles, they are consequently wholly devoid of brainpower,and have neither reflection, judgment nor forethought, and hardly anymemory. Hence, in their fits of fury, they remember no claims and recog-

nize no distinctions. I have actually known a case where a Woman hasexterminated her whole household, and half an hour afterwards, whenher rage was over and the fragments swept away, has asked what has

become of her husband and children.Obviously then a Woman is not to be irritated as long as she is in a po-

sition where she can turn round. When you have them in their apart-mentswhich are constructed with a view to denying them thatpoweryou can say and do what you like; for they are then wholly im-potent for mischief, and will not remember a few minutes hence the in-cident for which they may be at this moment threatening you with death,nor the promises which you may have found it necessary to make in or-der to pacify their fury.

On the whole we got on pretty smoothly in our domestic relations, ex-cept in the lower strata of the Military Classes. There the want of tact anddiscretion on the part of the husbands produces at times indescribabledisasters. Relying too much on the offensive weapons of their acuteangles instead of the defensive organs of good sense and seasonable sim-ulations, these reckless creatures too often neglect the prescribed

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construction of the women's apartments, or irritate their wives by ill-ad-vised expressions out of doors, which they refuse immediately to retract.Moreover a blunt and stolid regard for literal truth indisposes them tomake those lavish promises by which the more judicious Circle can in a

moment pacify his consort. The result is massacre; not, however, withoutits advantages, as it eliminates the more brutal and troublesome of theIsosceles; and by many of our Circles the destructiveness of the ThinnerSex is regarded as one among many providential arrangements for sup-pressing redundant population, and nipping Revolution in the bud.

Yet even in our best regulated and most approximately Circular famil-ies I cannot say that the ideal of family life is so high as with you inSpaceland. There is peace, in so far as the absence of slaughter may becalled by that name, but there is necessarily little harmony of tastes or

pursuits; and the cautious wisdom of the Circles has ensured safety atthe cost of domestic comfort. In every Circular or Polygonal household ithas been a habit from time immemorialand now has become a kind ofinstinct among the women of our higher classesthat the mothers anddaughters should constantly keep their eyes and mouths towards theirhusband and his male friends; and for a lady in a family of distinction toturn her back upon her husband would be regarded as a kind of portent,involving loss of STATUS. But, as I shall soon shew, this custom, thoughit has the advantage of safety, is not without disadvantages.

In the house of the Working Man or respectable Tradesmanwherethe wife is allowed to turn her back upon her husband, while pursuingher household avocationsthere are at least intervals of quiet, when thewife is neither seen nor heard, except for the humming sound of thecontinuous Peace-cry; but in the homes of the upper classes there is toooften no peace. There the voluble mouth and bright penetrating eye areever directed toward the Master of the household; and light itself is notmore persistent than the stream of Feminine discourse. The tact and skillwhich suffice to avert a Woman's sting are unequal to the task of stop-ping a Woman's mouth; and as the wife has absolutely nothing to say,and absolutely no constraint of wit, sense, or conscience to prevent herfrom saying it, not a few cynics have been found to aver that they preferthe danger of the death-dealing but inaudible sting to the safe sonorous-ness of a Woman's other end.

To my readers in Spaceland the condition of our Women may seentruly deplorable, and so indeed it is. A Male of the lowest type of the Iso-sceles may look forward to some improvement of his angle, and to theultimate elevation of the whole of his degraded caste; but no Woman can

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entertain such hopes for her sex. "Once a Woman, always a Woman" is aDecree of Nature; and the very Laws of Evolution seem suspended inher disfavour. Yet at least we can admire the wise Prearrangement whichhas ordained that, as they have no hopes, so they shall have no memory

to recall, and no forethought to anticipate, the miseries and humiliationswhich are at once a necessity of their existence and the basis of the con-stitution of Flatland.

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Chapter 5Of our Methods of Recognizing one another

You, who are blessed with shade as well as light, you, who are giftedwith two eyes, endowed with a knowledge of perspective, and charmedwith the enjoyment of various colours, you, who can actually SEE an

angle, and contemplate the complete circumference of a Circle in thehappy region of the Three Dimensions how shall I make it clear to youthe extreme difficulty which we in Flatland experience in recognizingone another's configuration?

Recall what I told you above. All beings in Flatland, animate and inan-imate, no matter what their form, present TO OUR VIEW the same, ornearly the same, appearance, viz. that of a straight Line. How then canone be distinguished from another, where all appear the same?

The answer is threefold. The first means of recognition is the sense of

hearing; which with us is far more highly developed than with you, andwhich enables us not only to distinguish by the voice of our personalfriends, but even to discriminate between different classes, at least so faras concerns the three lowest orders, the Equilateral, the Square, and thePentagonfor the Isosceles I take no account. But as we ascend the so-cial scale, the process of discriminating and being discriminated by hear-ing increases in difficulty, partly because voices are assimilated, partly

because the faculty of voice-discrimination is a plebeian virtue not muchdeveloped among the Aristocracy. And wherever there is any danger of

imposture we cannot trust to this method. Amongst our lowest orders,the vocal organs are developed to a degree more than correspondentwith those of hearing, so that an Isosceles can easily feign the voice of aPolygon, and, with some training, that of a Circle himself. A secondmethod is therefore more commonly resorted to.

FEELING is, among our Women and lower classesabout our upperclasses I shall speak presentlythe principal test of recognition, at allevents between strangers, and when the question is, not as to the indi-vidual, but as to the class. What therefore "introduction" is among the

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higher classes in Spaceland, that the process of "feeling" is with us. "Per-mit me to ask you to feel and be felt by my friend Mr. So-and-so"isstill, among the more old-fashioned of our country gentlemen in districtsremote from towns, the customary formula for a Flatland introduction.

But in the towns, and among men of business, the words "be felt by" areomitted and the sentence is abbreviated to, "Let me ask you to feel Mr.So-and-so"; although it is assumed, of course, that the "feeling" is to bereciprocal. Among our still more modern and dashing young gentle-menwho are extremely averse to superfluous effort and supremely in-different to the purity of their native languagethe formula is still fur-ther curtailed by the use of "to feel" in a technical sense, meaning, "torecommend-for- the-purposes-of-feeling-and-being-felt"; and at this mo-ment the "slang" of polite or fast society in the upper classes sanctions

such a barbarism as "Mr. Smith, permit me to feel Mr. Jones."Let not my Reader however suppose that "feeling" is with us the tedi-

ous process that it would be with you, or that we find it necessary to feelright round all the sides of every individual before we determine theclass to which he belongs. Long practice and training, begun in theschools and continued in the experience of daily life, enable us to dis-criminate at once by the sense of touch, between the angles of an equal-sided Triangle, Square, and Pentagon; and I need not say that the brain-less vertex of an acute-angled Isosceles is obvious to the dullest touch. It

is therefore not necessary, as a rule, to do more than feel a single angle ofan individual; and this, once ascertained, tells us the class of the personwhom we are addressing, unless indeed he belongs to the higher sec-tions of the nobility. There the difficulty is much greater. Even a Masterof Arts in our University of Wentbridge has been known to confuse aten-sided with a twelve-sided Polygon; and there is hardly a Doctor ofScience in or out of that famous University who could pretend to decidepromptly and unhesitatingly between a twenty-sided and a twenty-foursided member of the Aristocracy.

Those of my readers who recall the extracts I gave above from the Le-gislative code concerning Women, will readily perceive that the processof introduction by contact requires some care and discretion. Otherwisethe angles might inflict on the unwary Feeling irreparable injury. It is es-sential for the safety of the Feeler that the Felt should stand perfectlystill. A start, a fidgety shifting of the position, yes, even a violent sneeze,has been known before now to prove fatal to the incautious, and to nip inthe bud many a promising friendship. Especially is this true among thelower classes of the Triangles. With them, the eye is situated so far from

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their vertex that they can scarcely take cognizance of what goes on atthat extremity of their frame. They are, moreover, of a rough coarsenature, not sensitive to the delicate touch of the highly organized Poly-gon. What wonder then if an involuntary toss of the head has ere now

deprived the State of a valuable life!I have heard that my excellent Grandfatherone of the least irregular

of his unhappy Isosceles class, who indeed obtained, shortly before hisdecease, four out of seven votes from the Sanitary and Social Board forpassing him into the class of the Equal-sided often deplored, with atear in his venerable eye, a miscarriage of this kind, which had occurredto his great-great-great-Grandfather, a respectable Working Man with anangle or brain of 59 degrees 30 minutes. According to his account, myunfortunately Ancestor, being afflicted with rheumatism, and in the act

of being felt by a Polygon, by one sudden start accidentally transfixedthe Great Man through the diagonal and thereby, partly in consequenceof his long imprisonment and degradation, and partly because of themoral shock which pervaded the whole of my Ancestor's relations, threw

back our family a degree and a half in their ascent towards better things.The result was that in the next generation the family brain was registeredat only 58 degrees, and not till the lapse of five generations was the lostground recovered, the full 60 degrees attained, and the Ascent from theIsosceles finally achieved. And all this series of calamities from one little

accident in the process of Feeling.As this point I think I hear some of my better educated readers ex-

claim, "How could you in Flatland know anything about angles and de-grees, or minutes? We SEE an angle, because we, in the region of Space,can see two straight lines inclined to one another; but you, who can seenothing but on straight line at a time, or at all events only a number of

bits of straight lines all in one straight line, how can you ever discernan angle, and much less register angles of different sizes?"

I answer that though we cannot SEE angles, we can INFER them, andthis with great precision. Our sense of touch, stimulated by necessity,and developed by long training, enables us to distinguish angles farmore accurately than your sense of sight, when unaided by a rule ormeasure of angles. nor must I omit to explain that we have great naturalhelps. It is with us a Law of Nature that the brain of the Isosceles classshall begin at half a degree, or thirty minutes, and shall increase (if it in-creases at all) by half a degree in every generation until the goal of 60 de-grees is reached, when the condition of serfdom is quitted, and the free-man enters the class of Regulars.

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Consequently, Nature herself supplies us with an ascending scale orAlphabet of angles for half a degree up to 60 degrees, Specimen of whichare placed in every Elementary School throughout the land. Owing to oc-casional retrogressions, to still more frequent moral and intellectual stag-

nation, and to the extraordinary fecundity of the Criminal and Vagabondclasses, there is always a vast superfluity of individuals of the half de-gree and single degree class, and a fair abundance of Specimens up to 10degrees. These are absolutely destitute of civil rights; and a great numberof them, not having even intelligence enough for the purposes of war-fare, are devoted by the States to the service of education. Fettered im-movably so as to remove all possibility of danger, they are placed in theclassrooms of our Infant Schools, and there they are utilized by the Boardof Education for the purpose of imparting to the offspring of the Middle

Classes the tact and intelligence which these wretched creatures them-selves are utterly devoid.

In some States the Specimens are occasionally fed and suffered to existfor several years; but in the more temperate and better regulated regions,it is found in the long run more advantageous for the educational in-terests of the young, to dispense with food, and to renew the Specimensevery monthwhich is about the average duration of the foodless exist-ence of the Criminal class. In the cheaper schools, what is gained by thelonger existence of the Specimen is lost, partly in the expenditure for

food, and partly in the diminished accuracy of the angles, which are im-paired after a few weeks of constant "feeling." Nor must we forget toadd, in enumerating the advantages of the more expensive system, that ittends, though slightly yet perceptibly, to the diminution of the redund-ant Isosceles population an object which every statesman in Flatlandconstantly keeps in view. On the whole thereforealthough I am not ig-norant that, in many popularly elected School Boards, there is a reactionin favour of "the cheap system" as it is called I am myself disposed tothink that this is one of the many cases in which expense is the truesteconomy.

But I must not allow questions of School Board politics to divert mefrom my subject. Enough has been said, I trust, to shew that Recognition

by Feeling is not so tedious or indecisive a process as might have beensupposed; and it is obviously more trustworthy than Recognition byhearing. Still there remains, as has been pointed out above, the objectionthat this method is not without danger. For this reason many in theMiddle and Lower classes, and all without exception in the Polygonal

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and Circular orders, prefer a third method, the description of which shallbe reserved for the next section.

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Chapter 6Of Recognition by Sight

I am about to appear very inconsistent. In the previous sections I havesaid that all figures in Flatland present the appearance of a straight line;and it was added or implied, that it is consequently impossible to distin-

guish by the visual organ between individuals of different classes: yetnow I am about to explain to my Spaceland critics how we are able to re-cognize one another by the sense of sight.

If however the Reader will take the trouble to refer to the passage inwhich Recognition by Feeling is stated to be universal, he will find thisqualification"among the lower classes." It is only among the higherclasses and in our more temperate climates that Sight Recognition ispractised.

That this power exists in any regions and for any classes is the result of

Fog; which prevails during the greater part of the year in all parts savethe torrid zones. That which is with you in Spaceland an unmixed evil,

blotting out the landscape, depressing the spirits, and enfeebling thehealth, is by us recognized as a blessing scarcely inferior to air itself, andas the Nurse of arts and Parent of sciences. But let me explain my mean-ing, without further eulogies on this beneficent Element.

If Fog were non-existent, all lines would appear equally and indistin-guishably clear; and this is actually the case in those unhappy countriesin which the atmosphere is perfectly dry and transparent. But wherever

there is a rich supply of Fog, objects that are at a distance, say of threefeet, are appreciably dimmer than those at the distance of two feet eleveninches; and the result is that by careful and constant experimental obser-vation of comparative dimness and clearness, we are enabled to inferwith great exactness the configuration of the object observed.

An instance will do more than a volume of generalities to make mymeaning clear.

Suppose I see two individuals approaching whose rank I wish to as-certain. They are, we will suppose, a Merchant and a Physician, or in

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other words, an Equilateral Triangle and a Pentagon; how am I to distin-guish them?

It will be obvious, to every child in Spaceland who has touched thethreshold of Geometrical Studies, that, if I can bring my eye so that its

glance may bisect an angle (A) of the approaching stranger, my view willlie as it were evenly between the two sides that are next to me (viz. CAand AB), so that I shall contemplate the two impartially, and both willappear of the same size.

Now in the case of (1) the Merchant, what shall I see? I shall see astraight line DAE, in which the middle point (A) will be very bright be-cause it is nearest to me; but on either side the line will shade awayRAPIDLY TO DIMNESS, because the sides AC and AB RECEDERAPIDLY INTO THE FOG and what appear to me as the Merchant's ex-

tremities, viz. D and E, will be VERY DIM INDEED.On the other hand in the case of (2) the Physician, though I shall here

also see a line (D'A'E') with a bright centre (A'), yet it will shade awayLESS RAPIDLY to dimness, because the sides (A'C', A'B') RECEDE LESSRAPIDLY INTO THE FOG: and what appear to me the Physician's ex-tremities, viz. D' and E', will not be NOT SO DIM as the extremities ofthe Merchant.

The Reader will probably understand from these two instances howafter a very long training supplemented by constant experience it is

possible for the well-educated classes among us to discriminate with fairaccuracy between the middle and lowest orders, by the sense of sight. Ifmy Spaceland Patrons have grasped this general conception, so far as toconceive the possibility of it and not to reject my account as altogetherincredibleI shall have attained all I can reasonably expect. Were I to at-tempt further details I should only perplex. Yet for the sake of the youngand inexperienced, who may perchance inferfrom the two simple in-stances I have given above, of the manner in which I should recognizemy Father and my Sonsthat Recognition by sight is an easy affair, itmay be needful to point out that in actual life most of the problems ofSight Recognition are far more subtle and complex.

If for example, when my Father, the Triangle, approaches me, he hap-pens to present his side to me instead of his angle, then, until I haveasked him to rotate, or until I have edged my eye around him, I am forthe moment doubtful whether he may not be a Straight Line, or, in otherwords, a Woman. Again, when I am in the company of one of my twohexagonal Grandsons, contemplating one of his sides (AB) full front, itwill be evident from the accompanying diagram that I shall see one

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whole line (AB) in comparative brightness (shading off hardly at all atthe ends) and two smaller lines (CA and BD) dim throughout and shad-ing away into greater dimness towards the extremities C and D.

But I must not give way to the temptation of enlarging on these topics.

The meanest mathematician in Spaceland will readily believe me when Iassert that the problems of life, which present themselves to the well-educatedwhen they are themselves in motion, rotating, advancing orretreating, and at the same time attempting to discriminate by the senseof sight between a number of Polygons of high rank moving in differentdirections, as for example in a ball-room or conversazionemust be of anature to task the angularity of the most intellectual, and amply justifythe rich endowments of the Learned Professors of Geometry, both Staticand Kinetic, in the illustrious University of Wentbridge, where the

Science and Art of Sight Recognition are regularly taught to large classesof the ELITE of the States.

It is only a few of the scions of our noblest and wealthiest houses, whoare able to give the time and money necessary for the thorough prosecu-tion of this noble and valuable Art. Even to me, a Mathematician of nomean standing, and the Grandfather of two most hopeful and perfectlyregular Hexagons, to find myself in the midst of a crowd of rotatingPolygons of the higher classes, is occasionally very perplexing. And ofcourse to a common Tradesman, or Serf, such a sight is almost as unintel-

ligible as it would be to you, my Reader, were you suddenly transportedto my country.

In such a crowd you could see on all sides of you nothing but a Line,apparently straight, but of which the parts would vary irregularly andperpetually in brightness or dimness. Even if you had completed yourthird year in the Pentagonal and Hexagonal classes in the University,and were perfect in the theory of the subject, you would still find therewas need of many years of experience, before you could move in a fash-ionable crowd without jostling against your betters, whom it is againstetiquette to ask to "feel," and who, by their superior culture and breed-ing, know all about your movements, while you know very little or noth-ing about theirs. in a word, to comport oneself with perfect propriety inPolygonal society, one ought to be a Polygon oneself. Such at least is thepainful teaching of my experience.

It is astonishing how much the Artor I may almost call it instinctof Sight Recognition is developed by the habitual practice of it and bythe avoidance of the custom of "Feeling." Just as, with you, the deaf anddumb, if once allowed to gesticulate and to use the hand-alphabet, will

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never acquire the more difficult but far more valuable art of lip-speechand lip-reading, so it is with us as regards "Seeing" and "Feeling." Nonewho in early life resort to "Feeling" will ever learn "Seeing" in perfection.

For this reason, among our Higher Classes, "Feeling" is discouraged or

absolutely forbidden. From the cradle their children, instead of going tothe Public Elementary schools (where the art of Feeling is taught,) aresent to higher Seminaries of an exclusive character; and at our illustriousUniversity, to "feel" is regarded as a most serious fault, involving Rustic-ation for the first offence, and Expulsion for the second.

But among the lower classes the art of Sight Recognition is regarded asan unattainable luxury. A common Tradesman cannot afford to let hissun spend a third of his life in abstract studies. The children of the poorare therefore allowed to "feel" from their earliest years, and they gain

thereby a precocity and an early vivacity which contrast at first most fa-vourably with the inert, undeveloped, and listless behaviour of the half-instructed youths of the Polygonal class; but when the latter have at lastcompleted their University course, and are prepared to put their theoryinto practice, the change that comes over them may almost be describedas a new birth, and in every art, science, and social pursuit they rapidlyovertake and distance their Triangular competitors.

Only a few of the Polygonal Class fail to pass the Final Test or LeavingExamination at the University. The condition of the unsuccessful minor-

ity is truly pitiable. Rejected from the higher class,, they are also despisedby the lower. They have neither the matured and systematically trainedpowers of the Polygonal Bachelors and Masters of Arts, nor yet the nat-ive precocity and mercurial versatility of the youthful Tradesman. Theprofessions, the public services, are closed against them, and though inmost States they are not actually debarred from marriage, yet they havethe greatest difficulty in forming suitable alliances, as experience shewsthat the offspring of such unfortunate and ill-endowed parents is gener-ally itself unfortunate, if not positively Irregular.

It is from these specimens of the refuse of our Nobility that the greatTumults and Seditions of past ages have generally derived their leaders;and so great is the mischief thence arising that an increasing minority ofour more progressive Statesmen are of opinion that true mercy woulddictate their entire suppression, by enacting that all who fail to pass theFinal Examination of the University should be either imprisoned for life,or extinguished by a painless death.

But I find myself digressing into the subject of Irregularities, a matterof such vital interest that it demands a separate section.

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Chapter 7Concerning Irregular Figures

Throughout the previous pages I have been assumingwhat perhapsshould have been laid down at the beginning as a distinct and funda-mental propositionthat every human being in Flatland is a Regular

Figure, that is to say of regular construction. By this I mean that a Wo-man must not only be a line, but a straight line; that an Artisan or Soldiermust have two of his sides equal; that Tradesmen must have three sidesequal; Lawyers (of which class I am a humble member), four sides equal,and, generally, that in every Polygon, all the sides must be equal.

The sizes of the sides would of course depend upon the age of the in-dividual. A Female at birth would be about an inch long, while a talladult Woman might extend to a foot. As to the Males of every class, itmay be roughly said that the length of an adult's size, when added to-

gether, is two feet or a little more. But the size of our sides is not underconsideration. I am speaking of the EQUALITY of sides, and it does notneed much reflection to see that the whole of the social life in Flatlandrests upon the fundamental fact that Nature wills all Figures to havetheir sides equal.

If our sides were unequal our angles might be unequal. Instead of itsbeing sufficient to feel, or estimate by sight, a single angle in order to de-termine the form of an individual, it would be necessary to ascertaineach angle by the experiment of Feeling. But life would be too short for

such a tedious groping. The whole science and art of Sight Recognitionwould at once perish; Feeling, so far as it is an art, would not long sur-vive; intercourse would become perilous or impossible; there would bean end to all confidence, all forethought; no one would be safe in makingthe most simple social arrangements; in a word, civilization might re-lapse into barbarism.

Am I going too fast to carry my Readers with me to these obvious con-clusions? Surely a moment's reflection, and a single instance from com-mon life, must convince every one that our social system is based upon

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Regularity, or Equality of Angles. You meet, for example, two or threeTradesmen in the street, whom your recognize at once to be Tradesman

by a glance at their angles and rapidly bedimmed sides, and you askthem to step into your house to lunch. This you do at present with per-

fect confidence, because everyone knows to an inch or two the area occu-pied by an adult Triangle: but imagine that your Tradesman drags be-hind his regular and respectable vertex, a parallelogram of twelve orthirteen inches in diagonal:what are you to do with such a monstersticking fast in your house door?

But I am insulting the intelligence of my Readers by accumulating de-tails which must be patent to everyone who enjoys the advantages of aResidence in Spaceland. Obviously the measurements of a single anglewould no longer be sufficient under such portentous circumstances;

one's whole life would be taken up in feeling or surveying the perimeterof one's acquaintances. Already the difficulties of avoiding a collision ina crowd are enough to tax the sagacity of even a well-educated Square;

but if no one could calculate the Regularity of a single figure in the com-pany, all would be chaos and confusion, and the slightest panic wouldcause serious injuries, orif there happened to be any Women or Sol-diers present perhaps considerable loss of life.

Expediency therefore concurs with Nature in stamping the seal of itsapproval upon Regularity of conformation: nor has the Law been back-

ward in seconding their efforts. "Irregularity of Figure" means with usthe same as, or more than, a combination of moral obliquity and crimin-ality with you, and is treated accordingly. There are not wanting, it istrue, some promulgators of paradoxes who maintain that there is no ne-cessary connection between geometrical and moral Irregularity. "The Ir-regular," they say, "is from his birth scouted by his own parents, derided

by his brothers and sisters, neglected by the domestics, scorned and sus-pected by society, and excluded from all posts of responsibility, trust,and useful activity. His every movement is jealously watched by the po-lice till he comes of age and presents himself for inspection; then he iseither destroyed, if he is found to exceed the fixed margin of deviation,at an uninteresting occupation for a miserable stipend; obliged to liveand board at the office, and to take even his vacation under close super-vision; what wonder that human nature, even in the best and purest, isembittered and perverted by such surroundings!"

All this very plausible reasoning does not convince me, as it has notconvinced the wisest of our Statesmen, that our ancestors erred in layingit down as an axiom of policy that the toleration of Irregularity is

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incompatible with the safety of the State. Doubtless, the life of an Irregu-lar is hard; but the interests of the Greater Number require that it shall behard. If a man with a triangular front and a polygonal back were allowedto exist and to propagate a still more Irregular posterity, what would be-

come of the arts of life? Are the houses and doors and churches in Flat-land to be altered in order to accommodate such monsters? Are ourticket-collectors to be required to measure every man's perimeter beforethey allow him to enter a theatre, or to take his place in a lecture room? Isan Irregular to be exempted from the militia? And if not, how is he to beprevented from carrying desolation into the ranks of his comrades?Again, what irresistible temptations to fraudulent impostures mustneeds beset such a creature! How easy for him to enter a shop with hispolygonal front foremost, and to order goods to any extent from a con-

fiding tradesman! Let the advocates of a falsely called Philanthropyplead as they may for the abrogation of the Irregular Penal Laws, I formy part have never known an Irregular who was not also what Natureevidently intended him to bea hypocrite, a misanthropist, and, up tothe limits of his power, a perpetrator of all manner of mischief.

Not that I should be disposed to recommend (at present) the extrememeasures adopted by some States, where an infant whose angle deviates

by half a degree from the correct angularity is summarily destroyed atbirth. Some of our highest and ablest men, men of real genius, have dur-

ing their earliest days laboured under deviations as great as, or evengreater than forty-five minutes: and the loss of their precious lives wouldhave been an irreparable injury to the State. The art of healing also hasachieved some of its most glorious triumphs in the compressions, exten-sions, trepannings, colligations, and other surgical or diaetetic operations

by which Irregularity has been partly or wholly cured. Advocating there-fore a VIA MEDIA, I would lay down no fixed or absolute line of de-marcation; but at the period when the frame is just beginning to set, andwhen the Medical Board has reported that recovery is improbably, Iwould suggest that the Irregular offspring be painlessly and mercifullyconsumed.

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Chapter 8Of the Ancient Practice of Painting

If my Readers have followed me with any attention up to this point, theywill not be surprised to hear that life is somewhat dull in Flatland. I donot, of course, mean that there are not battles, conspiracies, tumults, fac-

tions, and all those other phenomena which are supposed to make His-tory interesting; nor would I deny that the strange mixture of the prob-lems of life and the problems of Mathematics, continually inducing con-

jecture and giving an opportunity of immediate verification, imparts toour existence a zest which you in Spaceland can hardly comprehend. Ispeak now from the aesthetic and artistic point of view when I say thatlife with us is dull; aesthetically and artistically, very dull indeed.

How can it be otherwise, when all one's prospect, all one's landscapes,historical pieces, portraits, flowers, still life, are nothing but a single line,

with no varieties except degrees of brightness and obscurity?It was not always thus. Colour, if Tradition speaks the truth, once for

the space of half a dozen centuries or more, threw a transient splendourover the lives of our ancestors in the remotest ages. Some private indi-viduala Pentagon whose name is variously reported having casuallydiscovered the constituents of the simpler colours and a rudimentarymethod of painting, is said to have begun by decorating first his house,then his slaves, then his Father, his Sons, and Grandsons, lastly himself.The convenience as well as the beauty of the results commended them-

selves to all. Wherever Chromatistes,for by that name the most trust-worthy authorities concur in calling him,turned his variegated frame,there he at once excited attention, and attracted respect. No one nowneeded to "feel" him; no one mistook his front for his back; all his move-ments were readily ascertained by his neighbours without the slighteststrain on their powers of calculation; no one jostled him, or failed tomake way for him; his voice was saved the labour of that exhausting ut-terance by which we colourless Squares and Pentagons are often forced

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to proclaim our individuality when we move amid a crowd of ignorantIsosceles.

The fashion spread like wildfire. Before a week was over, every Squareand Triangle in the district had copied the example of Chromatistes, and

only a few of the more conservative Pentagons still held out. A month ortwo found even the Dodecagons infected with the innovation. A yearhad not elapsed before the habit had spread to all but the very highest ofthe Nobility. Needless to say, the custom soon made its way from thedistrict of Chromatistes to surrounding regions; and within two genera-tions no one in all Flatland was colourless except the Women and thePriests.

Here Nature herself appeared to erect a barrier, and to plead againstextending the innovations to these two classes. Many- sidedness was al-

most essential as a pretext for the Innovators. "Distinction of sides is in-tended by Nature to imply distinction of colours"such was the soph-ism which in those days flew from mouth to mouth, converting wholetowns at a time to a new culture. But manifestly to our Priests and Wo-men this adage did not apply. The latter had only one side, and there-foreplurally and pedantically speakingNO SIDES. The formerif atleast they would assert their claim to be readily and truly Circles, andnot mere high-class Polygons, with an infinitely large number of infin-itesimally small sides were in the habit of boasting (what Women con-

fessed and deplored) that they also had no sides, being blessed with aperimeter of only one line, or, in other words, a Circumference. Hence itcame to pass that these two Classes could see no force in the so-called ax-iom about "Distinction of Sides implying Distinction of Colour;" andwhen all others had succumbed to the fascinations of corporal decora-tion, the Priests and the Women alone still remained pure from the pol-lution of paint.

Immoral, licentious, anarchical, unscientificcall them by what namesyou willyet, from an aesthetic point of view, those ancient days of theColour Revolt were the glorious childhood of Art in Flatland a child-hood, alas, that never ripened into manhood, nor even reached the blos-som of youth. To live then in itself a delight, because living implied see-ing. Even at a small party, the company was a pleasure to behold; therichly varied hues of the assembly in a church or theatre are said to havemore than once proved too distracting from our greatest teachers andactors; but most ravishing of all is said to have been the unspeakablemagnificence of a military review.

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The sight of a line of battle of twenty thousand Isosceles suddenly fa-cing about, and exchanging the sombre black of their bases for the or-ange of the two sides including their acute angle; the militia of the Equi-lateral Triangles tricoloured in red, white, and blue; the mauve, ultra-

marine, gamboge, and burnt umber of the Square artillerymen rapidlyrotating near their vermillion guns; the dashing and flashing of the five-coloured and six-coloured Pentagons and Hexagons careering across thefield in their offices of surgeons, geometricians and aides-de-campallthese may well have been sufficient to render credible the famous storyhow an illustrious Circle, overcome by the artistic beauty of the forcesunder his command, threw aside his marshal's baton and his royalcrown, exclaiming that he henceforth exchanged them for the artist'spencil. How great and glorious the sensuous development of these days

must have been is in part indicated by the very language and vocabularyof the period. The commonest utterances of the commonest citizens inthe time of the Colour Revolt seem to have been suffused with a richertinge of word or thought; and to that era we are even now indebted forour finest poetry and for whatever rhythm still remains in the more sci-entific utterance of those modern days.

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Chapter 9Of the Universal Colour Bill

But meanwhile the intellectual Arts were fast decaying.The Art of Sight Recognition, being no longer needed, was no longer

practised; and the studies of Geometry, Statics, Kinetics, and other

kindred subjects, came soon to be considered superfluous, and feel intodisrespect and neglect even at our University. The inferior Art of Feelingspeedily experienced the same fate at our Elementary Schools. Then theIsosceles classes, asserting that the Specimens were no longer used norneeded, and refusing to pay the customary tribute from the Criminalclasses to the service of Education, waxed daily more numerous andmore insolent on the strength of their immunity from the old burdenwhich had formerly exercised the twofold wholesome effect of at oncetaming their brutal nature and thinning their excessive numbers.

Year by year the Soldiers and Artisans began more vehemently to as-sertand with increasing truththat there was no great difference

between them and the very highest class of Polygons, now that theywere raised to an equality with the latter, and enabled to grapple with allthe difficulties and solve all the problems of life, whether Statical orKinetical, by the simple process of Colour Recognition. Not content withthe natural neglect into which Sight Recognition was falling, they began

boldly to demand the legal prohibition of all "monopolizing and aristo-cratic Arts" and the consequent abolition of all endowments for the stud-

ies of Sight Recognition, Mathematics, and Feeling. Soon, they began toinsist that inasmuch as Colour, which was a second Nature, had des-troyed the need of aristocratic distinctions, the Law should follow in thesame path, and that henceforth all individuals and all classes should berecognized as absolutely equal and entitled to equal rights.

Finding the higher Orders wavering and undecided, the leaders of theRevolution advanced still further in their requirements, and at last de-manded that all classes alike, the Priests and the Women not excepted,should do homage to Colour by submitting to be painted. When it was

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objected that Priests and Women had no sides, they retorted that Natureand Expediency concurred in dictating that the front half of every hu-man being (that is to say, the half containing his eye and mouth) should

be distinguishable from his hinder half. They therefore brought before a

general and extraordinary Assembly of all the States of Flatland a Billproposing that in every Woman the half containing the eye and mouthshould be coloured red, and the other half green. The Priests were to bepainted in the same way, red being applied to that semicircle in whichthe eye and mouth formed the middle point; while the other or hindersemicircle was to be coloured green.

There was no little cunning in this proposal, which indeed emanatednot from any Isoscelesfor no being so degraded would have angularityenough to appreciate, much less to devise, such a model of state-craft

but from an Irregular Circle who, instead of being destroyed in his child-hood, was reserved by a foolish indulgence to bring desolation on hiscountry and destruction on myriads of followers.

On the one hand the proposition was calculated to bring the Womenin all classes over to the side of the Chromatic Innovation. For by assign-ing to the Women the same two colours as were assigned to the Priests,the Revolutionists thereby ensured that, in certain positions, every Wo-man would appear as a Priest, and be treated with corresponding respectand deferencea prospect that could not fail to attract the Female Sex in

a mass.But by some of my Readers the possibility of the identical appearance

of Priests and Women, under a new Legislation, may not be recognized;if so, a word or two will make it obvious.

Imagine a woman duly decorated, according to the new Code; withthe front half (i.e., the half containing the eye and mouth) red, and withthe hinder half green. Look at her from one side. Obviously you will seea straight line, HALF RED, HALF GREEN.

Now imagine a Priest, whose mouth is at M, and whose front semi-circle (AMB) is consequently coloured red, while his hinder semicircle isgreen; so that the diameter AB divides the green from the red. If you con-template the Great Man so as to have your eye in the same straight lineas his dividing diameter (AB), what you will see will be a straight line(CBD), of which ONE HALF (CB) WILL BE RED, AND THE OTHER(BD) GREEN. The whole line (CD) will be rather shorter perhaps thanthat of a full-sized Woman, and will shade off more rapidly towards itsextremities; but the identity of the colours would give you an immediateimpression of identity in Class, making you neglectful of other details.

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Bear in mind the decay of Sight Recognition which threatened society atthe time of the Colour revolt; add too the certainty that Woman wouldspeedily learn to shade off their extremities so as to imitate the Circles; itmust then be surely obvious to you, my dear Reader, that the Colour Bill

placed us under a great danger of confounding a Priest with a youngWoman.

How attractive this prospect must have been to the Frail Sex may read-ily be imagined. They anticipated with delight the confusion that wouldensue. At home they might hear political and ecclesiastical secrets inten-ded not for them but for their husbands and brothers, and might even is-sue some commands in the name of a priestly Circle; out of doors thestriking combination of red and green without addition of any other col-ours, would be sure to lead the common people into endless mistakes,

and the Woman would gain whatever the Circles lost, in the deference ofthe passers by. As for the scandal that would befall the Circular Class ifthe frivolous and unseemly conduct of the Women were imputed tothem, and as to the consequent subversion of the Constitution, the Fe-male Sex could not be expected to give a thought to these considerations.Even in the households of the Circles, the Women were all in favour ofthe Universal Colour Bill.

The second object aimed at by the Bill was the gradual demoralizationof the Circles themselves. In the general intellectual decay they still pre-

served their pristine clearness and strength of understanding. From theirearliest childhood, familiarized in their Circular households with thetotal absence of Colour, the Nobles alone preserved the Sacred Art ofSight Recognition, with all the advantages that result from that admir-able training of the intellect. Hence, up to the date of the introduction ofthe Universal Colour Bill, the Circles had not only held their own, buteven increased their lead of the other classes by abstinence from the pop-ular fashion.

Now therefore the artful Irregular whom I described above as the realauthor of this diabolical Bill, determined at one blow to lower the statusof the Hierarchy by forcing them to submit to the pollution of Colour,and at the same time to destroy their domestic opportunities of trainingin the Art of Sight Recognition, so as to enfeeble their intellects by de-priving them of their pure and colourless homes. Once subjected to thechromatic taint, every parental and every childish Circle would demoral-ize each other. Only in discerning between the Father and the Motherwould the Circular infant find problems for the exercise of his under-standingproblems too often likely to be corrupted by maternal

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impostures with the result of shaking the child's faith in all logical con-clusions. Thus by degrees the intellectual lustre of the Priestly Orderwould wane, and the road would then lie open for a total destruction ofall Aristocratic Legislature and for the subversion of our Privileged

Classes.

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Chapter 10Of the Suppression of the Chromatic Sedition

The agitation for the Universal Colour Bill continued for three years; andup to the last moment of that period it seemed as though Anarchy weredestined to triumph.

A whole army of Polygons, who turned out to fight as private soldiers,was utterly annihilated by a superior force of Isosceles Triangles theSquares and Pentagons meanwhile remaining neutral.

Worse than all, some of the ablest Circles fell a prey to conjugal fury.Infuriated by political animosity, the wives in many a noble householdwearied their lords with prayers to give up their opposition to the Col-our Bill; and some, finding their entreaties fruitless, fell on andslaughtered their innocent children and husband, perishing themselvesin the act of carnage. It is recorded that during that triennial agitation no

less than twenty-three Circles perished in domestic discord.Great indeed was the peril. It seemed as though the Priests had no

choice between submission and extermination; when suddenly thecourse of events was completely changed by one of those picturesque in-cidents which Statesmen ought never to neglect, often to anticipate, andsometimes perhaps to originate, because of the absurdly disproportion-ate power with which they appeal to the sympathies of the populace.

It happened that an Isosceles of a low type, with a brain little if at allabove four degreesaccidentally dabbling in the colours of some

Tradesman whose shop he had plunderedpainted himself, or causedhimself to be painted (for the story varies) with the twelve colours of aDodecagon. Going into the Market Place he accosted in a feigned voice amaiden, the orphan daughter of a noble Polygon, whose affection informer days he had sought in vain; and by a series of deceptionsaided,on the one side, by a string of lucky accidents too long to relate, and, onthe other, by an almost inconceivable fatuity and neglect of ordinary pre-cautions on the part of the relations of the bridehe succeeded in

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consummating the marriage. The unhappy girl committed suicide ondiscovering the fraud to which she had been subjected.

When the news of this catastrophe spread from State to State theminds of the Women were violently agitated. Sympathy with the miser-

able victim and anticipations of similar deceptions for themselves, theirsisters, and their daughters, made them now regard the Colour Bill in anentirely new aspect. Not a few openly avowed themselves converted toantagonism; the rest needed only a slight stimulus to make a similaravowal. Seizing this favourable opportunity, the Circles hastily con-vened an extraordinary Assembly of the States; and besides the usualguard of Convicts, they secured the attendance of a large number of re-actionary Women.

Amidst an unprecedented concourse, the Chief Circle of those days

by name Pantocyclusarose to find himself hissed and hooted by ahundred and twenty thousand Isosceles. But he secured silence by de-claring that henceforth the Circles would enter on a policy of Concession;yielding to the wishes of the majority, they would accept the Colour Bill.The uproar being at once converted to applause, he invited Chroma-tistes, the leader of the Sedition, into the centre of the hall, to receive inthe name of his followers the submission of the Hierarchy. Then fol-lowed a speech, a masterpiece of rhetoric, which occupied nearly a dayin the delivery, and to which no summary can do justice.

With a grave appearance of impartiality he declared that as they werenow finally committing themselves to Reform or Innovation, it was de-sirable that they should take one last view of the perimeter of the wholesubject, its defects as well as its advantages. Gradually introduction themention of the dangers to the Tradesmen, the Professional Classes andthe Gentlemen, he silenced the rising murmurs of the Isosceles by re-minding them that, in spite of all these defects, he was willing to acceptthe Bill if it was approved by the majority. But it was manifest that all,except the Isosceles, were moved by his words and were either neutral oraverse to the Bill.

Turning now to the Workmen he asserted that their interests must notbe neglected, and that, if they intended to accept the Colour Bill, theyought at least to do so with full view of the consequences. Many of them,he said, were on the point of being admitted to the class of the RegularTriangles; others anticipated for their children a distinction they couldnot hope for themselves. That honourable ambition would not have to besacrificed. With the universal adoption of Colour, all distinctions wouldcease; Regularity would be confused with Irregularity; development

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would give place to retrogression; the Workman would in a few genera-tions be degraded to the level of the Military, or even the Convict Class;political power would be in the hands of the greatest number, that is tosay the Criminal Classes, who were already more numerous than the

Workmen, and would soon out-number all the other Classes put togeth-er when the usual Compensative Laws of Nature were violated.

A subdued murmur of assent ran through the ranks of the Artisans,and Chromatistes, in alarm, attempted to step forward and addressthem. But he found himself encompassed with guards and forced to re-main silent while the Chief Circle in a few impassioned words made a fi-nal appeal to the Women, exclaiming that, if the Colour Bill passed, nomarriage would henceforth be safe, no woman's honour secure; fraud,deception, hypocrisy would pervade every household; domestic bliss

would share the fate of the Constitution and pass to speedy perdition."Sooner than this," he cried, "Come death."

At these words, which were the preconcerted signal for action, the Iso-sceles Convicts fell on and transfixed the wretched Chromatistes; theRegular Classes, opening their ranks, made way for a band of Womenwho, under direction of the Circles, moved back foremost, invisibly andunerringly upon the unconscious soldiers; the Artisans, imitating the ex-ample of their betters, also opened their ranks. Meantime bands of Con-victs occupied every entrance with an impenetrable phalanx.

The battle, or rather carnage, was of short duration. Under the skillfulgeneralship of the Circles almost every Woman's charge was fatal andvery many extracted their sting uninjured, ready for a second slaughter.But no second blow was needed; the rabble of the Isosceles did the restof the business for themselves. Surprised, leader-less, attacked in front

by invisible foes, and finding egress cut off by the Convicts behind them,they at once after their mannerlost all presence of mind, and raisedthe cry of "treachery." This sealed their fate. Every Isosceles now saw andfelt a foe in every other. In half an hour not one of that vast multitudewas living; and the fragments of seven score thousand of the CriminalClass slain by one another's angles attested the triumph of Order.

The Circles delayed not to push their victory to the uttermost. TheWorking Men they spared but decimated. The Militia of the Equilateralswas at once called out, and every Triangle suspected of Irregularity onreasonable grounds, was destroyed by Court Martial, without the form-ality of exact measurement by the Social Board. The homes of the Milit-ary and Artisan classes were inspected in a course of visitation extendingthrough upwards of a year; and during that period every town, village,

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and hamlet was systematically purged of that excess of the lower orderswhich had been brought about by the neglect to pay the tribute of Crim-inals to the Schools and University, and by the violation of other naturalLaws of the Constitution of Flatland. Thus the balance of classes was

again restored.Needless to say that henceforth the use of Colour was abolished, and

its possession prohibited. Even the utterance of any word denoting Col-our, except by the Circles or by qualified scientific teachers, was pun-ished by a severe penalty. Only at our University in some of the veryhighest and most esoteric classeswhich I myself have never been priv-ileged to attendit is understood that the sparing use of Colour is stillsanctioned for the purpose of illustrating some of the deeper problems ofmathematics. But of this I can only speak from hearsay.

Elsewhere in Flatland, Colour is no non-existent. The art of making itis known to only one living person, the Chief Circle for the time being;and by him it is handed down on his death-bed to none but his Suc-cessor. One manufactory alone produces it; and, lest the secret should be

betrayed, the Workmen are annually consumed, and fresh ones intro-duced. So great is the terror with which even now our Aristocracy looks

back to the far-distant days of the agitation for the Universal Colour Bill.

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Chapter 11Concerning our Priests

It is high time that I should pass from these brief and discursive notesabout things in Flatland to the central event of this book, my initiationinto the mysteries of Space. THAT is my subject; all that has gone before

is merely preface.For this reason I must omit many matters of which the explanation

would not, I flatter myself, be without interest for my Readers: as for ex-ample, our method of propelling and stopping ourselves, although desti-tute of feet; the means by which we give fixity to structures of wood,stone, or brick, although of course we have no hands, nor can we layfoundations as you can, nor avail ourselves of the lateral pressure of theearth; the manner in which the rain originates in the intervals betweenour various zones, so that the northern regions do not intercept the mois-

ture falling on the southern; the nature of our hills and mines, our treesand vegetables, our seasons and harvests; our Alphabet and method ofwriting, adapted to our linear tablets; these and a hundred other detailsof our physical existence I must pass over, nor do I mention them nowexcept to indicate to my readers that their omission proceeds not fromforgetfulness on the part of the author, but from his regard for the timeof the Reader.

Yet before I proceed to my legitimate subject some few final remarkswill no doubt be expected by my Readers upon these pillars and main-

stays of the Constitution of Flatland, the controllers of our conduct andshapers of our destiny, the objects of universal homage and almost of ad-oration: need I say that I mean our Circles or Priests?

When I call them Priests, let me not be understood as meaning nomore than the term denotes with you. With us, our Priests are Adminis-trators of all Business, Art, and Science; Directors of Trade, Commerce,Generalship, Architecture, Engineering, Education, Statesmanship, Le-gislature, Morality, Theology; doing nothing themselves, they are theCauses of everything worth doing, that is done by others.

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Although popularly everyone called a Circle is deemed a Circle, yetamong the better educated Classes it is known that no Circle is really aCircle, but only a Polygon with a very large number of very small sides.As the number of the sides increases, a Polygon approximates to a Circle;

and, when the number is very great indeed, say for example three orfour hundred, it is extremely difficult for the most delicate touch to feelany polygonal angles. Let me say rather it WOULD be difficult: for, as Ihave shown above, Recognition by Feeling is unknown among thehighest society, and to FEEL a Circle would be considered a most auda-cious insult. This habit of abstention from Feeling in the best society en-ables a Circle the more easily to sustain the veil of mystery in which,from his earliest years, he is wont to enwrap the exact nature of his Peri-meter or Circumference. Three feet being the average Perimeter it fol-

lows that, in a Polygon of three hundred sides each side will be no morethan the hundredth part of a foot in length, or little more than the tenthpart of an inch; and in a Polygon of six or seven hundred sides the sidesare little larger than the diameter of a Spaceland pin-head. It is alwaysassumed, by courtesy, that the Chief Circle for the time being has tenthousand sides.

The ascent of the posterity of the Circles in the social scale is not re-stricted, as it is among the lower Regular classes, by the Law of Naturewhich limits the increase of sides to one in each generation. If it were so,

the number of sides in the Circle would be a mere question of pedigreeand arithmetic, and the four hundred and ninety-seventh descendant ofan Equilateral Triangle would necessarily be a polygon with five hun-dred sides. But this is not the case. Nature's Law prescribes two antagon-istic decrees affecting Circular propagation; first, that as the race climbshigher in the scale of development, so development shall proceed at anaccelerated pace; second, that in the same proportion, the race shall be-come less fertile. Consequently in the home of a Polygon of four or fivehundred sides it is rare to find a son; more than one is never seen. On theother hand the son of a five-hundred-sided Polygon has been known topossess five hundred and fifty, or even six hundred sides.

Art also steps in to help the process of higher Evolution. Our physi-cians have discovered that the small and tender sides of an infant Poly-gon of the higher class can be fractured, and his whole frame re-set, withsuch exactness that a Polygon of two or three hundred sides some-timesby no means always, for the process is attended with seriousriskbut sometimes overleaps two or three hundred generations, and as

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it were double at a stroke, the number of his progenitors and the nobilityof his descent.

Many a promising child is sacrificed in this way. Scarcely one out often survives. Yet so strong is the parental ambition among those Poly-

gons who are, as it were, on the fringe of the Circular class, that it is veryrare to find the Nobleman of that position in society, who has neglectedto place his first-born in the Circular Neo-Therapeutic Gymnasium be-fore he has attained the age of a month.

One year determines success or failure. At the end of that time thechild has, in all probability, added one more to the tombstones thatcrowd the Neo-Therapeutic Cemetery; but on rare occasional a glad pro-cession bares back the little one to his exultant parents, no longer a Poly-gon, but a Circle, at least by courtesy: and a singl

Abbott - Flatland a Romance of Many Dimensions

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